MinT - Best Known (8, 8+64, s)-Nets in Base 128

Best Known (8, 8+64, s)-Nets in Base 128

(8, 8+64, 216)-Net over F₁₂₈ — Constructive and digital

Digital (8, 72, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 72, 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]

(8, 8+64, 276)-Net over F₁₂₈ — Digital

Digital (8, 72, 276)-net over F₁₂₈, using

net from sequence [i] based on digital (8, 275)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 8 and N(F) ≥ 276, using
  - a curve from the manYPoints database [i]

(8, 8+64, 5534)-Net in Base 128 — Upper bound on s

There is no (8, 72, 5535)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 52 575645 895891 750265 842143 819908 526309 607974 144529 099621 522780 501019 674349 612382 329612 113486 312641 770495 188053 943191 062320 520754 305787 104065 213776 799820 > 128⁷² [i]