MinT - Best Known (244−113, 244, s)-Nets in Base 4

Best Known (244−113, 244, s)-Nets in Base 4

(244−113, 244, 130)-Net over F₄ — Constructive and digital

Digital (131, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(244−113, 244, 218)-Net over F₄ — Digital

Digital (131, 244, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−113, 244, 2919)-Net in Base 4 — Upper bound on s

There is no (131, 244, 2920)-net in base 4, because

1 times m-reduction [i] would yield (131, 243, 2920)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 203 066274 081131 507898 364896 197337 445965 104448 950760 684521 638151 770253 661778 446724 005332 452900 626405 227738 904477 981456 013835 697980 662726 976513 293720 > 4²⁴³ [i]