MinT - Best Known (130−75, 130, s)-Nets in Base 8

Best Known (130−75, 130, s)-Nets in Base 8

(130−75, 130, 98)-Net over F₈ — Constructive and digital

Digital (55, 130, 98)-net over F₈, using

t-expansion [i] based on digital (37, 130, 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]

(130−75, 130, 144)-Net over F₈ — Digital

Digital (55, 130, 144)-net over F₈, using

t-expansion [i] based on digital (45, 130, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(130−75, 130, 2924)-Net in Base 8 — Upper bound on s

There is no (55, 130, 2925)-net in base 8, because

1 times m-reduction [i] would yield (55, 129, 2925)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 318 903476 787174 028157 694554 191895 629791 751834 237994 764275 386598 593743 600855 646822 238176 383577 623930 252679 347657 078720 > 8¹²⁹ [i]