MinT - Best Known (243−109, 243, s)-Nets in Base 4

Best Known (243−109, 243, s)-Nets in Base 4

(243−109, 243, 130)-Net over F₄ — Constructive and digital

Digital (134, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(243−109, 243, 240)-Net over F₄ — Digital

Digital (134, 243, 240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−109, 243, 3443)-Net in Base 4 — Upper bound on s

There is no (134, 243, 3444)-net in base 4, because

1 times m-reduction [i] would yield (134, 242, 3444)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 381514 120576 392266 640745 627092 889389 320965 929056 858780 913743 259431 676502 800747 255361 020348 137766 023920 220710 290962 792066 309329 709017 410882 271952 > 4²⁴² [i]