MinT - Best Known (260−116, 260, s)-Nets in Base 4

Best Known (260−116, 260, s)-Nets in Base 4

(260−116, 260, 134)-Net over F₄ — Constructive and digital

Digital (144, 260, 134)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (13, 71, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. digital (73, 189, 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]

(260−116, 260, 260)-Net over F₄ — Digital

Digital (144, 260, 260)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−116, 260, 3693)-Net in Base 4 — Upper bound on s

There is no (144, 260, 3694)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 460952 132494 021774 168763 071765 523286 772842 878860 579136 180605 073004 790526 794067 096121 068082 625667 276142 967553 317267 487605 826450 893585 647743 751479 965184 144728 > 4²⁶⁰ [i]