MinT - Best Known (53, 53+104, s)-Nets in Base 8

Best Known (53, 53+104, s)-Nets in Base 8

(53, 53+104, 98)-Net over F₈ — Constructive and digital

Digital (53, 157, 98)-net over F₈, using

t-expansion [i] based on digital (37, 157, 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]

(53, 53+104, 144)-Net over F₈ — Digital

Digital (53, 157, 144)-net over F₈, using

t-expansion [i] based on digital (45, 157, 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]

(53, 53+104, 1506)-Net in Base 8 — Upper bound on s

There is no (53, 157, 1507)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6100 605534 979858 161058 054115 191503 294550 642436 632200 865670 106593 645323 055524 134265 973294 209432 239341 709874 792607 169980 364623 054775 155103 105264 > 8¹⁵⁷ [i]