MinT - Best Known (257−154, 257, s)-Nets in Base 4

Best Known (257−154, 257, s)-Nets in Base 4

(257−154, 257, 104)-Net over F₄ — Constructive and digital

Digital (103, 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]

(257−154, 257, 144)-Net over F₄ — Digital

Digital (103, 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]

(257−154, 257, 942)-Net in Base 4 — Upper bound on s

There is no (103, 257, 943)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 56120 439254 644246 685141 477747 037073 757494 594500 683052 347810 029646 032525 292158 131241 878641 013566 117235 309478 702429 942008 278805 571325 105214 259103 541537 773380 > 4²⁵⁷ [i]