MinT - Best Known (179−117, 179, s)-Nets in Base 4

Best Known (179−117, 179, s)-Nets in Base 4

(179−117, 179, 66)-Net over F₄ — Constructive and digital

Digital (62, 179, 66)-net over F₄, using

t-expansion [i] based on digital (49, 179, 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]

(179−117, 179, 99)-Net over F₄ — Digital

Digital (62, 179, 99)-net over F₄, using

t-expansion [i] based on digital (61, 179, 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]

(179−117, 179, 480)-Net in Base 4 — Upper bound on s

There is no (62, 179, 481)-net in base 4, because

1 times m-reduction [i] would yield (62, 178, 481)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150944 376775 795660 734093 173852 348552 519619 852477 168885 879735 337353 899019 329066 852461 570604 953297 656161 403808 > 4¹⁷⁸ [i]