MinT - Best Known (213−134, 213, s)-Nets in Base 4

Best Known (213−134, 213, s)-Nets in Base 4

(213−134, 213, 104)-Net over F₄ — Constructive and digital

Digital (79, 213, 104)-net over F₄, using

t-expansion [i] based on digital (73, 213, 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]

(213−134, 213, 112)-Net over F₄ — Digital

Digital (79, 213, 112)-net over F₄, using

t-expansion [i] based on digital (73, 213, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(213−134, 213, 651)-Net in Base 4 — Upper bound on s

There is no (79, 213, 652)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 183 850625 227535 184452 077472 512733 242720 394501 867461 740962 451905 416753 090290 263093 830984 414870 298549 926243 166101 520322 827467 581850 > 4²¹³ [i]