MinT - Best Known (116, 116+56, s)-Nets in Base 4

Best Known (116, 116+56, s)-Nets in Base 4

(116, 116+56, 240)-Net over F₄ — Constructive and digital

Digital (116, 172, 240)-net over F₄, using

4¹ times duplication [i] based on digital (115, 171, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 57, 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]

(116, 116+56, 528)-Net over F₄ — Digital

Digital (116, 172, 528)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+56, 18781)-Net in Base 4 — Upper bound on s

There is no (116, 172, 18782)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 875098 078892 563406 978867 624481 163454 894001 882549 936905 115911 218549 993000 443765 525557 968844 632743 176561 > 4¹⁷² [i]