MinT - Best Known (260−127, 260, s)-Nets in Base 4

Best Known (260−127, 260, s)-Nets in Base 4

(260−127, 260, 130)-Net over F₄ — Constructive and digital

Digital (133, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(260−127, 260, 195)-Net over F₄ — Digital

Digital (133, 260, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−127, 260, 2367)-Net in Base 4 — Upper bound on s

There is no (133, 260, 2368)-net in base 4, because

1 times m-reduction [i] would yield (133, 259, 2368)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 864961 822820 489787 393449 247813 515581 313160 861062 061804 741811 524805 543987 292503 855594 658504 826026 992650 962909 733200 997431 007002 480902 326785 490755 547014 504695 > 4²⁵⁹ [i]