MinT - Best Known (128, 128+132, s)-Nets in Base 4

Best Known (128, 128+132, s)-Nets in Base 4

(128, 128+132, 130)-Net over F₄ — Constructive and digital

Digital (128, 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]

(128, 128+132, 176)-Net over F₄ — Digital

Digital (128, 260, 176)-net over F₄, using

t-expansion [i] based on digital (125, 260, 176)-net over F₄, using
- net from sequence [i] based on digital (125, 175)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 125 and N(F) ≥ 176, using
    - Drinfeld modules of rank 1 [i]

(128, 128+132, 1940)-Net in Base 4 — Upper bound on s

There is no (128, 260, 1941)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 543971 657405 029934 492377 676690 528766 431571 462537 028558 491226 881493 078051 533170 558871 102250 188666 677325 274388 980047 761992 092839 713605 201934 083372 091404 488764 > 4²⁶⁰ [i]