MinT - Best Known (255−147, 255, s)-Nets in Base 4

Best Known (255−147, 255, s)-Nets in Base 4

(255−147, 255, 130)-Net over F₄ — Constructive and digital

Digital (108, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(255−147, 255, 144)-Net over F₄ — Digital

Digital (108, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 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]

(255−147, 255, 1102)-Net in Base 4 — Upper bound on s

There is no (108, 255, 1103)-net in base 4, because

1 times m-reduction [i] would yield (108, 254, 1103)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 879 451943 819240 650525 592668 193182 441193 740578 951267 140421 387288 792774 459032 944232 536292 651625 920041 181935 786003 142325 472250 071695 391501 468518 406244 692930 > 4²⁵⁴ [i]