MinT - Best Known (99, 99+148, s)-Nets in Base 4

Best Known (99, 99+148, s)-Nets in Base 4

(99, 99+148, 104)-Net over F₄ — Constructive and digital

Digital (99, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(99, 99+148, 144)-Net over F₄ — Digital

Digital (99, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(99, 99+148, 907)-Net in Base 4 — Upper bound on s

There is no (99, 247, 908)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54140 979966 961611 256523 896389 664513 036256 271049 984848 636104 565667 334733 754838 445413 199963 814606 087496 687516 324642 554623 614985 932403 537647 172196 509550 > 4²⁴⁷ [i]