MinT - Best Known (12, 68, s)-Nets in Base 128

Best Known (12, 68, s)-Nets in Base 128

(12, 68, 288)-Net over F₁₂₈ — Constructive and digital

Digital (12, 68, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 68, 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, 68, 321)-Net over F₁₂₈ — Digital

Digital (12, 68, 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, 68, 11646)-Net in Base 128 — Upper bound on s

There is no (12, 68, 11647)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 195285 928057 008205 779474 152006 514539 987474 225811 127738 114896 415778 172122 074520 042655 341988 976573 479581 444134 497445 287791 127941 663874 793581 302693 > 128⁶⁸ [i]