MinT - Best Known (105, 222, s)-Nets in Base 4

Best Known (105, 222, s)-Nets in Base 4

(105, 222, 130)-Net over F₄ — Constructive and digital

Digital (105, 222, 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]

(105, 222, 144)-Net over F₄ — Digital

Digital (105, 222, 144)-net over F₄, using

t-expansion [i] based on digital (91, 222, 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]

(105, 222, 1425)-Net in Base 4 — Upper bound on s

There is no (105, 222, 1426)-net in base 4, because

1 times m-reduction [i] would yield (105, 221, 1426)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 531643 286342 720580 291699 073433 685551 303541 417407 395173 790320 387336 260960 904722 085261 553140 118930 446965 041154 943631 601078 870820 538688 > 4²²¹ [i]