MinT - Best Known (106, 106+138, s)-Nets in Base 4

Best Known (106, 106+138, s)-Nets in Base 4

(106, 106+138, 130)-Net over F₄ — Constructive and digital

Digital (106, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(106, 106+138, 144)-Net over F₄ — Digital

Digital (106, 244, 144)-net over F₄, using

t-expansion [i] based on digital (91, 244, 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]

(106, 106+138, 1134)-Net in Base 4 — Upper bound on s

There is no (106, 244, 1135)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 842 505240 280543 770745 901294 827472 807681 178103 016772 524117 121488 613572 657367 018132 814088 586264 863183 644561 857137 314395 471938 482022 647315 241421 685078 > 4²⁴⁴ [i]