MinT - Best Known (238−159, 238, s)-Nets in Base 4

Best Known (238−159, 238, s)-Nets in Base 4

(238−159, 238, 104)-Net over F₄ — Constructive and digital

Digital (79, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(238−159, 238, 112)-Net over F₄ — Digital

Digital (79, 238, 112)-net over F₄, using

t-expansion [i] based on digital (73, 238, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(238−159, 238, 581)-Net in Base 4 — Upper bound on s

There is no (79, 238, 582)-net in base 4, because

1 times m-reduction [i] would yield (79, 237, 582)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49285 754669 739539 015773 783292 245170 947779 826520 056316 227333 764758 032658 712952 412777 739580 681255 239351 309758 691415 738294 527057 419311 891822 295808 > 4²³⁷ [i]