MinT - Best Known (229−107, 229, s)-Nets in Base 4

Best Known (229−107, 229, s)-Nets in Base 4

(229−107, 229, 130)-Net over F₄ — Constructive and digital

Digital (122, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 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]

(229−107, 229, 201)-Net over F₄ — Digital

Digital (122, 229, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−107, 229, 2627)-Net in Base 4 — Upper bound on s

There is no (122, 229, 2628)-net in base 4, because

1 times m-reduction [i] would yield (122, 228, 2628)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 187771 920308 140531 455254 272646 141333 612456 534999 704558 328883 614827 168231 801202 763754 001584 635229 958474 072451 849431 877533 714196 560682 277360 > 4²²⁸ [i]