MinT - Best Known (203−141, 203, s)-Nets in Base 4

Best Known (203−141, 203, s)-Nets in Base 4

(203−141, 203, 66)-Net over F₄ — Constructive and digital

Digital (62, 203, 66)-net over F₄, using

t-expansion [i] based on digital (49, 203, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(203−141, 203, 99)-Net over F₄ — Digital

Digital (62, 203, 99)-net over F₄, using

t-expansion [i] based on digital (61, 203, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(203−141, 203, 434)-Net in Base 4 — Upper bound on s

There is no (62, 203, 435)-net in base 4, because

1 times m-reduction [i] would yield (62, 202, 435)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 432858 414690 848972 969474 387814 690572 100280 731557 944140 464038 227317 426512 306242 488262 825945 360309 464243 634514 143388 321672 > 4²⁰² [i]