MinT - Best Known (243−149, 243, s)-Nets in Base 4

Best Known (243−149, 243, s)-Nets in Base 4

(243−149, 243, 104)-Net over F₄ — Constructive and digital

Digital (94, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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]

(243−149, 243, 144)-Net over F₄ — Digital

Digital (94, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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]

(243−149, 243, 820)-Net in Base 4 — Upper bound on s

There is no (94, 243, 821)-net in base 4, because

1 times m-reduction [i] would yield (94, 242, 821)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 249803 090422 629496 096551 555579 977652 705059 113334 053004 023089 070301 329675 852328 097447 529984 686313 545960 417202 081571 241090 792960 757636 484239 255568 > 4²⁴² [i]