MinT - Best Known (113, 200, s)-Nets in Base 4

Best Known (113, 200, s)-Nets in Base 4

(113, 200, 130)-Net over F₄ — Constructive and digital

Digital (113, 200, 130)-net over F₄, using

t-expansion [i] based on digital (105, 200, 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, 200, 223)-Net over F₄ — Digital

Digital (113, 200, 223)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 200, 3405)-Net in Base 4 — Upper bound on s

There is no (113, 200, 3406)-net in base 4, because

1 times m-reduction [i] would yield (113, 199, 3406)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 650979 000766 418799 868894 137436 111493 978762 163642 471735 182862 288202 033661 289011 660899 792059 952522 577786 478382 991153 652844 > 4¹⁹⁹ [i]