MinT - Best Known (78−60, 78, s)-Nets in Base 32

Best Known (78−60, 78, s)-Nets in Base 32

(78−60, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 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]

(78−60, 78, 128)-Net in Base 32 — Constructive

(18, 78, 128)-net in base 32, using

base change [i] based on digital (5, 65, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(78−60, 78, 161)-Net over F₃₂ — Digital

Digital (18, 78, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(78−60, 78, 3167)-Net in Base 32 — Upper bound on s

There is no (18, 78, 3168)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2535 932122 621429 684075 472767 557231 104190 225211 842439 260366 798003 417293 059029 866113 008506 339002 564616 208169 638590 934395 > 32⁷⁸ [i]