MinT - Best Known (113, 113+89, s)-Nets in Base 4

Best Known (113, 113+89, s)-Nets in Base 4

(113, 113+89, 130)-Net over F₄ — Constructive and digital

Digital (113, 202, 130)-net over F₄, using

t-expansion [i] based on digital (105, 202, 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+89, 216)-Net over F₄ — Digital

Digital (113, 202, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+89, 3200)-Net in Base 4 — Upper bound on s

There is no (113, 202, 3201)-net in base 4, because

1 times m-reduction [i] would yield (113, 201, 3201)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 353571 610720 750275 528922 256685 262717 154772 372501 062273 421861 310314 148900 367061 477681 273740 045171 059877 228820 569282 855712 > 4²⁰¹ [i]