MinT - Best Known (238−144, 238, s)-Nets in Base 4

Best Known (238−144, 238, s)-Nets in Base 4

(238−144, 238, 104)-Net over F₄ — Constructive and digital

Digital (94, 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]

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

Digital (94, 238, 144)-net over F₄, using

t-expansion [i] based on 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]

(238−144, 238, 842)-Net in Base 4 — Upper bound on s

There is no (94, 238, 843)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 203086 239661 494227 200063 360117 268816 058175 514330 337273 953261 145496 693308 150803 445729 132461 811547 440363 535466 621033 685385 860320 182796 327877 734785 > 4²³⁸ [i]