MinT - Best Known (233−101, 233, s)-Nets in Base 4

Best Known (233−101, 233, s)-Nets in Base 4

(233−101, 233, 130)-Net over F₄ — Constructive and digital

Digital (132, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(233−101, 233, 258)-Net over F₄ — Digital

Digital (132, 233, 258)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−101, 233, 3996)-Net in Base 4 — Upper bound on s

There is no (132, 233, 3997)-net in base 4, because

1 times m-reduction [i] would yield (132, 232, 3997)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 011013 342358 334991 308961 692168 521822 756465 978801 217907 028240 220798 550282 306770 069018 488256 185383 556534 644683 531198 334566 800720 129737 338056 > 4²³² [i]