MinT - Best Known (147−88, 147, s)-Nets in Base 8

Best Known (147−88, 147, s)-Nets in Base 8

(147−88, 147, 98)-Net over F₈ — Constructive and digital

Digital (59, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 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]

(147−88, 147, 144)-Net over F₈ — Digital

Digital (59, 147, 144)-net over F₈, using

t-expansion [i] based on digital (45, 147, 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]

(147−88, 147, 2536)-Net in Base 8 — Upper bound on s

There is no (59, 147, 2537)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 718503 727314 296112 892211 862575 045602 222502 727713 647022 453142 033453 810061 914824 407598 856048 659015 948658 804831 070426 491008 048622 800720 > 8¹⁴⁷ [i]