MinT - Best Known (132, 132+109, s)-Nets in Base 4

Best Known (132, 132+109, s)-Nets in Base 4

(132, 132+109, 130)-Net over F₄ — Constructive and digital

Digital (132, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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, 132+109, 232)-Net over F₄ — Digital

Digital (132, 241, 232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+109, 3268)-Net in Base 4 — Upper bound on s

There is no (132, 241, 3269)-net in base 4, because

1 times m-reduction [i] would yield (132, 240, 3269)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 126943 012519 371617 923876 361013 061927 256095 325995 206448 819433 621330 014786 791359 058236 843966 100569 172639 431182 642486 558632 260930 216795 578652 163424 > 4²⁴⁰ [i]