MinT - Best Known (103, 103+50, s)-Nets in Base 4

Best Known (103, 103+50, s)-Nets in Base 4

(103, 103+50, 240)-Net over F₄ — Constructive and digital

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]

(103, 103+50, 472)-Net over F₄ — Digital

Digital (103, 153, 472)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+50, 16389)-Net in Base 4 — Upper bound on s

There is no (103, 153, 16390)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 411033 646309 638685 059150 848556 768112 764896 077263 716518 391868 527783 161415 944115 371116 693504 > 4¹⁵³ [i]