MinT - Best Known (238−147, 238, s)-Nets in Base 4

Best Known (238−147, 238, s)-Nets in Base 4

(238−147, 238, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(238−147, 238, 144)-Net over F₄ — Digital

Digital (91, 238, 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]

(238−147, 238, 782)-Net in Base 4 — Upper bound on s

There is no (91, 238, 783)-net in base 4, because

1 times m-reduction [i] would yield (91, 237, 783)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52195 282236 092852 629406 378086 002410 832188 004546 509551 566477 957922 646447 805703 680489 747505 570566 747156 468945 734384 442439 318713 286008 256212 001000 > 4²³⁷ [i]