MinT - Best Known (132, 247, s)-Nets in Base 4

Best Known (132, 247, s)-Nets in Base 4

(132, 247, 130)-Net over F₄ — Constructive and digital

Digital (132, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(132, 247, 217)-Net over F₄ — Digital

Digital (132, 247, 217)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 247, 2872)-Net in Base 4 — Upper bound on s

There is no (132, 247, 2873)-net in base 4, because

1 times m-reduction [i] would yield (132, 246, 2873)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12958 627119 235643 814389 037224 345365 429513 670546 345043 695782 249404 786757 585695 180244 347050 840214 018757 522426 252778 200692 293820 511377 760636 619923 437508 > 4²⁴⁶ [i]