MinT - Best Known (119−79, 119, s)-Nets in Base 8

Best Known (119−79, 119, s)-Nets in Base 8

(119−79, 119, 98)-Net over F₈ — Constructive and digital

Digital (40, 119, 98)-net over F₈, using

t-expansion [i] based on digital (37, 119, 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]

(119−79, 119, 129)-Net over F₈ — Digital

Digital (40, 119, 129)-net over F₈, using

t-expansion [i] based on digital (38, 119, 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]

(119−79, 119, 1163)-Net in Base 8 — Upper bound on s

There is no (40, 119, 1164)-net in base 8, because

1 times m-reduction [i] would yield (40, 118, 1164)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 37413 937974 189521 064059 597564 573947 198359 090021 735924 904502 788664 070344 217104 579817 670681 908117 036415 712040 > 8¹¹⁸ [i]