MinT - Best Known (88, 231, s)-Nets in Base 4

Best Known (88, 231, s)-Nets in Base 4

(88, 231, 104)-Net over F₄ — Constructive and digital

Digital (88, 231, 104)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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]

(88, 231, 129)-Net over F₄ — Digital

Digital (88, 231, 129)-net over F₄, using

t-expansion [i] based on digital (81, 231, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(88, 231, 753)-Net in Base 4 — Upper bound on s

There is no (88, 231, 754)-net in base 4, because

1 times m-reduction [i] would yield (88, 230, 754)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 093622 451962 438522 746957 020191 552926 479062 501177 949604 223896 112464 109336 416708 264439 142193 304788 476852 460661 728371 221374 725518 802856 736888 > 4²³⁰ [i]