MinT - Best Known (138−96, 138, s)-Nets in Base 8

Best Known (138−96, 138, s)-Nets in Base 8

(138−96, 138, 98)-Net over F₈ — Constructive and digital

Digital (42, 138, 98)-net over F₈, using

t-expansion [i] based on digital (37, 138, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(138−96, 138, 129)-Net over F₈ — Digital

Digital (42, 138, 129)-net over F₈, using

t-expansion [i] based on digital (38, 138, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(138−96, 138, 1026)-Net in Base 8 — Upper bound on s

There is no (42, 138, 1027)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42488 980778 817468 836898 197357 269633 144824 638855 253731 241187 757980 032283 622543 816529 889199 711744 686913 974871 391811 994539 968320 > 8¹³⁸ [i]