MinT - Best Known (260−125, 260, s)-Nets in Base 4

Best Known (260−125, 260, s)-Nets in Base 4

(260−125, 260, 130)-Net over F₄ — Constructive and digital

Digital (135, 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]

(260−125, 260, 205)-Net over F₄ — Digital

Digital (135, 260, 205)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−125, 260, 2560)-Net in Base 4 — Upper bound on s

There is no (135, 260, 2561)-net in base 4, because

1 times m-reduction [i] would yield (135, 259, 2561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 858555 681716 943125 767595 608904 860624 682631 716366 195337 957321 286760 477762 397794 178775 336783 347872 935176 216880 860455 184521 544796 882938 792652 115389 617382 192384 > 4²⁵⁹ [i]