MinT - Best Known (239−132, 239, s)-Nets in Base 4

Best Known (239−132, 239, s)-Nets in Base 4

(239−132, 239, 130)-Net over F₄ — Constructive and digital

Digital (107, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(239−132, 239, 144)-Net over F₄ — Digital

Digital (107, 239, 144)-net over F₄, using

t-expansion [i] based on digital (91, 239, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(239−132, 239, 1229)-Net in Base 4 — Upper bound on s

There is no (107, 239, 1230)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 815242 849845 385486 962496 970839 021023 629265 580890 783244 973320 170697 542135 012278 184890 493328 643028 082414 111512 002201 910903 768859 223364 668254 901194 > 4²³⁹ [i]