MinT - Best Known (257−155, 257, s)-Nets in Base 4

Best Known (257−155, 257, s)-Nets in Base 4

(257−155, 257, 104)-Net over F₄ — Constructive and digital

Digital (102, 257, 104)-net over F₄, using

t-expansion [i] based on digital (73, 257, 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]

(257−155, 257, 144)-Net over F₄ — Digital

Digital (102, 257, 144)-net over F₄, using

t-expansion [i] based on digital (91, 257, 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]

(257−155, 257, 924)-Net in Base 4 — Upper bound on s

There is no (102, 257, 925)-net in base 4, because

1 times m-reduction [i] would yield (102, 256, 925)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13930 665351 351529 298873 997635 712462 914193 474460 368166 752195 728040 629316 926390 725715 361914 590893 327901 355042 131957 730261 700916 675508 051830 541670 630225 681688 > 4²⁵⁶ [i]