MinT - Best Known (84, 84+160, s)-Nets in Base 4

Best Known (84, 84+160, s)-Nets in Base 4

(84, 84+160, 104)-Net over F₄ — Constructive and digital

Digital (84, 244, 104)-net over F₄, using

t-expansion [i] based on digital (73, 244, 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]

(84, 84+160, 129)-Net over F₄ — Digital

Digital (84, 244, 129)-net over F₄, using

t-expansion [i] based on digital (81, 244, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(84, 84+160, 635)-Net in Base 4 — Upper bound on s

There is no (84, 244, 636)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 826 997562 515676 769448 034710 138734 555763 222934 057849 367678 177149 809760 495573 037394 382356 253805 313189 119731 249943 531857 905700 583320 407784 383174 383255 > 4²⁴⁴ [i]