MinT - Best Known (113, 232, s)-Nets in Base 4

Best Known (113, 232, s)-Nets in Base 4

(113, 232, 130)-Net over F₄ — Constructive and digital

Digital (113, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(113, 232, 165)-Net over F₄ — Digital

Digital (113, 232, 165)-net over F₄, using

t-expansion [i] based on digital (109, 232, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(113, 232, 1683)-Net in Base 4 — Upper bound on s

There is no (113, 232, 1684)-net in base 4, because

1 times m-reduction [i] would yield (113, 231, 1684)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 153482 995004 046852 695549 148682 527873 198079 470637 011445 651663 615377 329066 406947 746708 524219 597488 975531 134598 985203 678448 383503 937175 589264 > 4²³¹ [i]