MinT - Best Known (127−72, 127, s)-Nets in Base 8

Best Known (127−72, 127, s)-Nets in Base 8

(127−72, 127, 98)-Net over F₈ — Constructive and digital

Digital (55, 127, 98)-net over F₈, using

t-expansion [i] based on digital (37, 127, 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]

(127−72, 127, 144)-Net over F₈ — Digital

Digital (55, 127, 144)-net over F₈, using

t-expansion [i] based on digital (45, 127, 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]

(127−72, 127, 3107)-Net in Base 8 — Upper bound on s

There is no (55, 127, 3108)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 960801 327702 488718 638947 024223 622677 103824 794909 384213 958586 030018 222513 378591 706107 123398 540291 506481 948681 113952 > 8¹²⁷ [i]