MinT - Best Known (131−75, 131, s)-Nets in Base 8

Best Known (131−75, 131, s)-Nets in Base 8

(131−75, 131, 98)-Net over F₈ — Constructive and digital

Digital (56, 131, 98)-net over F₈, using

t-expansion [i] based on digital (37, 131, 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]

(131−75, 131, 144)-Net over F₈ — Digital

Digital (56, 131, 144)-net over F₈, using

t-expansion [i] based on digital (45, 131, 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]

(131−75, 131, 3094)-Net in Base 8 — Upper bound on s

There is no (56, 131, 3095)-net in base 8, because

1 times m-reduction [i] would yield (56, 130, 3095)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2538 084418 987962 570253 646281 704516 256289 741973 070030 135993 755443 791902 063192 797115 331590 832768 454295 294033 002884 279488 > 8¹³⁰ [i]