MinT - Best Known (248−152, 248, s)-Nets in Base 4

Best Known (248−152, 248, s)-Nets in Base 4

(248−152, 248, 104)-Net over F₄ — Constructive and digital

Digital (96, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(248−152, 248, 144)-Net over F₄ — Digital

Digital (96, 248, 144)-net over F₄, using

t-expansion [i] based on digital (91, 248, 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]

(248−152, 248, 833)-Net in Base 4 — Upper bound on s

There is no (96, 248, 834)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214833 520225 439742 972205 128933 961769 112925 067126 425615 421565 446696 177425 088157 943395 320729 530370 030916 353413 498463 281113 227994 509103 518173 136805 747136 > 4²⁴⁸ [i]