MinT - Best Known (113, 208, s)-Nets in Base 4

Best Known (113, 208, s)-Nets in Base 4

(113, 208, 130)-Net over F₄ — Constructive and digital

Digital (113, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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, 208, 198)-Net over F₄ — Digital

Digital (113, 208, 198)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 208, 2706)-Net in Base 4 — Upper bound on s

There is no (113, 208, 2707)-net in base 4, because

1 times m-reduction [i] would yield (113, 207, 2707)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42358 454568 686232 962850 478321 789394 254223 641701 528060 800686 828652 215113 592119 190381 446947 153135 204371 860380 816015 436763 552000 > 4²⁰⁷ [i]