MinT - Best Known (98−65, 98, s)-Nets in Base 32

Best Known (98−65, 98, s)-Nets in Base 32

(98−65, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(98−65, 98, 216)-Net in Base 32 — Constructive

(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]

(98−65, 98, 273)-Net over F₃₂ — Digital

Digital (33, 98, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 98, 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]

(98−65, 98, 15049)-Net in Base 32 — Upper bound on s

There is no (33, 98, 15050)-net in base 32, because

1 times m-reduction [i] would yield (33, 97, 15050)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 959625 438523 707798 928085 315856 431692 365905 857887 530362 322350 801187 596041 286296 188159 946114 897522 793529 966572 943281 315795 460743 867834 314521 446378 > 32⁹⁷ [i]