MinT - Best Known (208−132, 208, s)-Nets in Base 4

Best Known (208−132, 208, s)-Nets in Base 4

(208−132, 208, 104)-Net over F₄ — Constructive and digital

Digital (76, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−132, 208, 112)-Net over F₄ — Digital

Digital (76, 208, 112)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−132, 208, 616)-Net in Base 4 — Upper bound on s

There is no (76, 208, 617)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186107 010380 606666 911917 868579 209121 183183 857649 402011 746551 514624 079698 452301 139725 205941 856218 502469 099194 681408 670704 559684 > 4²⁰⁸ [i]