MinT - Best Known (113, 113+147, s)-Nets in Base 4

Best Known (113, 113+147, s)-Nets in Base 4

(113, 113+147, 130)-Net over F₄ — Constructive and digital

Digital (113, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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, 113+147, 165)-Net over F₄ — Digital

Digital (113, 260, 165)-net over F₄, using

t-expansion [i] based on digital (109, 260, 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, 113+147, 1217)-Net in Base 4 — Upper bound on s

There is no (113, 260, 1218)-net in base 4, because

1 times m-reduction [i] would yield (113, 259, 1218)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 867406 387459 317344 435844 927060 999758 892643 513200 005176 538178 370595 721140 901531 534007 879642 253857 790963 195301 417337 769425 086364 731578 206879 648734 138000 175600 > 4²⁵⁹ [i]