MinT - Best Known (256−121, 256, s)-Nets in Base 4

Best Known (256−121, 256, s)-Nets in Base 4

(256−121, 256, 130)-Net over F₄ — Constructive and digital

Digital (135, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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]

(256−121, 256, 214)-Net over F₄ — Digital

Digital (135, 256, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−121, 256, 2749)-Net in Base 4 — Upper bound on s

There is no (135, 256, 2750)-net in base 4, because

1 times m-reduction [i] would yield (135, 255, 2750)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3379 431467 554306 805333 054712 981988 749812 346337 513727 355684 437366 708961 654443 455512 319224 139876 773690 950460 079126 923799 897122 384856 831653 395483 477511 440881 > 4²⁵⁵ [i]