MinT - Best Known (260−60, 260, s)-Nets in Base 4

Best Known (260−60, 260, s)-Nets in Base 4

(260−60, 260, 1048)-Net over F₄ — Constructive and digital

Digital (200, 260, 1048)-net over F₄, using

trace code for nets [i] based on digital (5, 65, 262)-net over F₂₅₆, using
- net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(260−60, 260, 3452)-Net over F₄ — Digital

Digital (200, 260, 3452)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−60, 260, 662986)-Net in Base 4 — Upper bound on s

There is no (200, 260, 662987)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 432490 945933 994852 610890 502951 131548 286356 634138 233322 441246 692600 667183 372874 279490 007826 523607 477228 946102 053466 617539 262959 349409 926307 048416 266297 252720 > 4²⁶⁰ [i]