MinT - Best Known (124, 208, s)-Nets in Base 4

Best Known (124, 208, s)-Nets in Base 4

(124, 208, 130)-Net over F₄ — Constructive and digital

Digital (124, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 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]

(124, 208, 293)-Net over F₄ — Digital

Digital (124, 208, 293)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 208, 5241)-Net in Base 4 — Upper bound on s

There is no (124, 208, 5242)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169686 103856 275815 528790 348760 620835 434877 234791 575005 244147 012761 011906 963835 979081 387248 984553 836769 074570 919820 080553 821040 > 4²⁰⁸ [i]