MinT - Best Known (34, 34+65, s)-Nets in Base 32

Best Known (34, 34+65, s)-Nets in Base 32

(34, 34+65, 120)-Net over F₃₂ — Constructive and digital

Digital (34, 99, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 99, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(34, 34+65, 216)-Net in Base 32 — Constructive

(34, 99, 216)-net in base 32, using

32¹ times duplication [i] based on (33, 98, 216)-net in base 32, using
- base change [i] based on digital (5, 70, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(34, 34+65, 273)-Net over F₃₂ — Digital

Digital (34, 99, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 99, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(34, 34+65, 16773)-Net in Base 32 — Upper bound on s

There is no (34, 99, 16774)-net in base 32, because

1 times m-reduction [i] would yield (34, 98, 16774)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3202 302622 228509 591569 305762 146202 787085 436034 944091 757559 923975 307408 705138 850974 006179 504640 340204 508393 221897 831826 760580 830331 633283 759992 416628 > 32⁹⁸ [i]