MinT - Best Known (12, 12+66, s)-Nets in Base 128

Best Known (12, 12+66, s)-Nets in Base 128

(12, 12+66, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 78, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 78, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(12, 12+66, 321)-Net over F₁₂₈ — Digital

Digital (12, 78, 321)-net over F₁₂₈, using

net from sequence [i] based on digital (12, 320)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 12 and N(F) ≥ 321, using
  - a curve from the manYPoints database [i]

(12, 12+66, 9897)-Net in Base 128 — Upper bound on s

There is no (12, 78, 9898)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 230 897743 980207 471368 110833 319054 022512 142235 745423 568727 843006 504536 918370 383553 437099 914297 424428 926785 995234 097351 585997 797642 678613 568201 282691 311718 638134 229823 > 128⁷⁸ [i]