MinT - Best Known (154−50, 154, s)-Nets in Base 4

Best Known (154−50, 154, s)-Nets in Base 4

(154−50, 154, 240)-Net over F₄ — Constructive and digital

Digital (104, 154, 240)-net over F₄, using

4¹ times duplication [i] based on digital (103, 153, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 51, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(154−50, 154, 486)-Net over F₄ — Digital

Digital (104, 154, 486)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−50, 154, 17325)-Net in Base 4 — Upper bound on s

There is no (104, 154, 17326)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 521 881780 856105 551029 833314 543963 418202 384944 110269 413134 030748 325709 731430 767382 449113 478298 > 4¹⁵⁴ [i]