MinT - Best Known (100, 100+157, s)-Nets in Base 4

Best Known (100, 100+157, s)-Nets in Base 4

(100, 100+157, 104)-Net over F₄ — Constructive and digital

Digital (100, 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]

(100, 100+157, 144)-Net over F₄ — Digital

Digital (100, 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]

(100, 100+157, 878)-Net in Base 4 — Upper bound on s

There is no (100, 257, 879)-net in base 4, because

1 times m-reduction [i] would yield (100, 256, 879)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13578 978078 896778 847735 947888 931674 153643 080454 350437 506266 532290 174462 292775 877157 806354 118688 374640 579400 192222 109932 279902 883404 300783 431336 806045 239983 > 4²⁵⁶ [i]