MinT - Best Known (51, 51+104, s)-Nets in Base 8

Best Known (51, 51+104, s)-Nets in Base 8

(51, 51+104, 98)-Net over F₈ — Constructive and digital

Digital (51, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(51, 51+104, 144)-Net over F₈ — Digital

Digital (51, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(51, 51+104, 1388)-Net in Base 8 — Upper bound on s

There is no (51, 155, 1389)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 96 483506 665920 470844 110093 231975 530556 920844 908018 581122 146841 217379 325483 417136 123135 231956 054666 648228 792526 332491 325624 322281 309625 598108 > 8¹⁵⁵ [i]