MinT - Best Known (243−111, 243, s)-Nets in Base 4

Best Known (243−111, 243, s)-Nets in Base 4

(243−111, 243, 130)-Net over F₄ — Constructive and digital

Digital (132, 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]

(243−111, 243, 227)-Net over F₄ — Digital

Digital (132, 243, 227)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−111, 243, 3125)-Net in Base 4 — Upper bound on s

There is no (132, 243, 3126)-net in base 4, because

1 times m-reduction [i] would yield (132, 242, 3126)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 633712 555562 542425 245770 768441 989828 881900 499125 646161 500741 453224 945039 820972 978757 155429 387291 325393 835880 058103 654020 471688 911095 726792 991024 > 4²⁴² [i]