MinT - Best Known (236−111, 236, s)-Nets in Base 4

Best Known (236−111, 236, s)-Nets in Base 4

(236−111, 236, 130)-Net over F₄ — Constructive and digital

Digital (125, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(236−111, 236, 202)-Net over F₄ — Digital

Digital (125, 236, 202)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−111, 236, 2612)-Net in Base 4 — Upper bound on s

There is no (125, 236, 2613)-net in base 4, because

1 times m-reduction [i] would yield (125, 235, 2613)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3082 296848 720472 381811 613320 072704 256149 155090 815988 698693 798579 608640 021364 470772 764978 286308 430649 313335 113346 263265 376887 251528 353551 183040 > 4²³⁵ [i]